My opinion:
Eevee as Scout (He would be the youngest and weakest like Scout)
Glaceon as Soldier (Head crest can kinda be like a helmet with flaps, second tankiest)
Flareon as Pyro (Obvious like you said)
Espeon as Demoman (Set off explosives with mind or summin idk)
Vaporeon as Heavy (The biggest tank, also fish with Russian accent funny)
Jolteon as Engineer (Electric weapons, and generally a technology theme)
Sylveon as Medic (Color pallets match well, innocent fairy/doctor but is actually crazy)
Leafeon as Sniper (The glasses bring out the eyes ig, would probably hide in a bush)
Umbreon as Spy (Dark and edgy vibes, fights dirty by nature)
And the shinies are BLU Team.